Tracing the cosmic web (1705.03021v1)

Abstract: The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -- depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper we bring twelve of these methods together and apply them to the same data set in order to understand how they compare. In general these cosmic web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore one would not {\it a priori} expect agreement between different techniques however, many of these methods do converge on the identification of specific features. In this paper we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. $M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) as being in filaments. Lastly, so that any future cosmic web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public.

Overview of Cosmic Web Classification Methods

The paper "Tracing the Cosmic Web" provides a comprehensive comparison of various methodologies employed to characterize the cosmic web—the intricate network formed by galaxies and dark matter on the largest scales in the universe. This paper is particularly pertinent for researchers involved in cosmology and large-scale structure, as it provides insight into the efficacy and limitations of different techniques used to trace the web-like patterns observed in cosmic matter distributions.

Methodological Classifications and Comparisons

The paper involves twelve distinct methods for cosmic web classification, categorizing them into several methodological families based on their underlying principles. These include:

1. Graph and Percolation Techniques: Representative of these techniques is the MST method, which utilizes minimal spanning trees to identify filamentary structures in galaxy surveys by focusing on connectedness.
2. Stochastic Methods: The Bisous model exemplifies the stochastic approach, employing a marked point process to detect filaments based on the geometric configuration of galaxies or haloes without requiring a density field.
3. Geometric, Hessian-based Methods: These methods, including T-web and V-web, utilize the Hessian matrix of the density or shear fields to identify web components based on the eigenvalues, distinguishing regions as voids, sheets, filaments, or knots.
4. Scale-space Multiscale Hessian-based Methods: The MMF/Nexus technique extends the single-scale approach by considering multiple scales to capture the hierarchical nature and finer details of the cosmic web structures.
5. Topological Methods: DisPerSE is a notable method in this category, relying on Morse theory to segment space and define cosmic web features through the singularities in the density field.
6. Phase-space Methods: ORIGAMI and MSWA are phase-space techniques that assess shell-crossing events to classify regions according to their collapse dimensionalities, identifying voids, sheets, filaments, and knots dynamically.

Key Findings

The comparison reveals significant variability across methods in the classification of cosmic web structures, reflecting the diverse strategies and objectives inherent in these techniques. Noteworthy findings include:

• Density Distribution: Despite the differences, methods show consensus in the progression of density distributions across cosmic web environments— with knots exhibiting higher densities, followed by filaments, sheets, and voids.
• Volume and Mass Fractions: Void regions consistently occupy the largest volume fraction, while knots contain a disproportionate mass relative to their volume. The disparities among methods in mass and volume fractions highlight the inherent complexities in defining web environments.
• Halo Environment Assignment: The paper discusses the classification of haloes by environment, noting substantial agreement among methods in categorizing massive haloes within knot regions, yet greater variability in filament and sheet assignments.

Implications and Future Directions

The paper underscores the importance of selecting appropriate cosmic web classification methods based on specific research goals, acknowledging that each method captures distinct aspects of the web-like cosmic structure. It opens avenues for further refinement and calibration of these methods against observational data, aimed at enhancing our understanding of the environmental influences on galaxy formation and evolution.

This research supports theoretical cosmology, providing a framework for integrating different methodological insights, and lays the groundwork for future studies that might explore the cosmic web's role in informing cosmological models and galaxy evolution theories. With ongoing advancements in computational techniques and observational tools, the potential for developing more sophisticated or unified approaches to cosmic web classification remains promising.